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a set is countable if it fits into Hilbert's Hotel, 'cause Hilbert's Hotel basically is the set of natural numbers in terms of the room numbers. So to be
equinumerous with a set of natural numbers is just the same thing as to fit into Hilbert's Hotel. And so what we've shown is that
if you have two countably infinite sets, then their union is also countably infinite. If you put them together and form a new set
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